Answered

Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

In 1992, South Dakota's population was 10 million. Since then, the population has grown by 1.4% each year. Based on this, when will the population reach 20 million?

Sagot :

fieryanswererft

Answer:

  • 49.9 years or 50 years later.
  • At year : 2042

Explanation:

use compound interest formula:  [tex]\sf \boxed{ \sf P ( \sf 1 + \dfrac{r}{100} )^n}[/tex]

[tex]\rightarrow \s \sf 10( 1 + \dfrac{1.4}{100} )^n = 20[/tex]

[tex]\rightarrow \sf ( 1.014) ^n = 2[/tex]

[tex]\rightarrow \sf n( ln( 1.014) ) = ln(2)[/tex]

[tex]\rightarrow\sf n = \dfrac{ln(2)}{ln( 1.014)}[/tex]

[tex]\rightarrow\sf n = 49.8563 \ years[/tex]

semsee45

Answer:

General form of an exponential equation:  [tex]y=ab^x[/tex]

where:

  • a is initial value
  • b is the base (or growth factor in decimal form)
  • x is the independent variable
  • y is the dependent variable
  • If b > 1 then it is an increasing function
  • If 0 < b < 1 then it is a decreasing function
  • Also b ≠ 0

Given information:

  • initial population = 10 million
  • growth rate = 1.4% each year

⇒ growth factor = 100% + 1.4% = 101.4% = 1.014

Inputting these values into the equation:

[tex]\implies y=10(1.014)^x[/tex]

where y is the population (in millions) and x is the number of years since 1992

Now all we need to do is set y = 20 and solve for x:

[tex]\implies 10(1.014)^x=20[/tex]

[tex]\implies 1.014^x=2[/tex]

[tex]\implies \ln 1.014^x=\ln 2[/tex]

[tex]\implies x\ln 1.014=\ln 2[/tex]

[tex]\implies x=\dfrac{\ln 2}{\ln 1.014}[/tex]

[tex]\implies x=49.85628343...[/tex]

1992 + x = 2041.8562....

Therefore, the population will reach 20 million during 2041, so the population will reach 20 million by 2042.

We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.